In order to verify the computing performance of the spiking neural P systems(SNPS)with the operational restriction,the min-sequentiality strategy is introduced into the standard SNPS to study its language generation ability. At each step of the calculation,only neurons satisfing the corresponding rules and containing the least number of spikes can be excited for the SNPS working in the min-sequentiality strategy. The relations between the SNPS working in the min-sequentiality strategy and the finite language and the regular language are analysed,and the mapping from the arbitrary multivariate alphabet to the binary alphabet is defined. The SNPS producing the recursively enumerable language is constructed. The addition module and the subtraction module are designed. By simulating the register machine,it is proved that the SNPS working in the min-sequentiality strategy can describe the recursively enumerable language and has the equivalent computing power to the Turing machine under the min-sequentiality strategy.